AF: Small: Collaborative Research: Geometric and Topological Algorithms for Analyzing Road Network Data

AF：小型：协作研究：用于分析道路网络数据的几何和拓扑算法

• 批准号: 1618605
• 负责人: Brittany Fasy
• 金额: $ 15.28万
• 依托单位: Montana State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2020-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1618605&HistoricalAwards=false
• 关键词: AF; Small; Collaborative; Research; Geometric

The project aims to develop theoretically grounded, effective methods for analyzing data associated with road networks -- using graphs that represent road networks as a framework for analyzing network data. Thanks to the spread of GPS-enabled devices, trajectory data has become ubiquitous. Many other sources, including census data and crime statistics, have addresses or geographic locations that link to an underlying road network. Algorithms with mathematical guarantees will be developed to align trajectories to the network under natural and realistic properties of true trajectories, to reconstruct road networks from trajectory and density data. It will also provide two frameworks for comparing data-endowed networks at different levels. While the problems of trajectory alignment, map reconstruction, and map comparison have attracted a lot of attention in the GIS community, most approaches are ad-hoc, provide no quality guarantees, and are limited to post-hoc analysis. This project will provide novel theoretical foundations combining approaches from computational topology and geometry, and will further advance the state-of-the-art of the field of topological / geometric data analysis. The PIs will continue to combine educational and research activities through this project. Students will be tightly integrated into the research and practical implementation of this project, and will be trained in integrating geometric thinking, algorithms development, and (trajectory) data analysis. The combination of such skills is increasingly important in data science. Topics involved in this project will enrich the course material and curriculum development at each of the three institutions.

该项目旨在开发理论上扎根的有效方法来分析与道路网络相关的数据 - 使用代表道路网络作为分析网络数据的框架的图表。多亏了启用GPS的设备的传播，轨迹数据已无处不在。 包括人口普查数据和犯罪统计在内的许多其他来源都有与基础道路网络相关的地址或地理位置。将开发具有数学保证的算法，以在真正的轨迹的自然和现实属性下与网络保持一致，从而从轨迹和密度数据中重建道路网络。它还将提供两个框架，用于比较不同级别的数据端网络。尽管轨迹一致性，地图重建和地图比较的问题在GIS社区中引起了很多关注，但大多数方法都是临时的，没有提供质量保证，并且仅限于事后分析。该项目将提供新的理论基础，结合了计算拓扑和几何形状的方法，并将进一步推进拓扑 /几何数据分析领域的最新领域。 PI将继续通过该项目结合教育和研究活动。学生将紧密整合到该项目的研究和实际实施中，并将在整合几何思维，算法开发和（轨迹）数据分析方面接受培训。在数据科学中，这种技能的结合越来越重要。该项目涉及的主题将丰富三个机构中每个机构的课程材料和课程开发。

项目成果

Towards Directed Collapsibility (Research)

走向定向可折叠性（研究）

• DOI: 10.1007/978-3-030-42687-3_17
• 发表时间: 2020
• 期刊: Association for Women in Mathematics series
• 作者: Belton, R.;Brooks, R.;Ebli, S.;Fajstrup, L;Fasy, B.T.;Ray, C.;Sanderson, N.;Vidaurre, E.
• 通讯作者: Vidaurre, E.

Comparing Directed and Weighted Road Maps

比较定向路线图和加权路线图

• DOI: 10.1007/978-3-319-89593-2_4
• 发表时间: 2018
• 期刊: Association for Women in Mathematics series
• 作者: Bittner, Alyson;Fasy, Brittany Terese;Grudzien, Maia;Hajra, Sayonita Ghosh;Huang, Jici;Pelatt, Kristine;Thatcher, Courtney;Tumurbaatar, Altansuren;Wenk, Carola
• 通讯作者: Wenk, Carola

Functional summaries of persistence diagrams

• DOI: 10.1007/s41468-020-00048-w
• 发表时间: 2020-01-01
• 期刊: J Appl Comput Topol
• 作者: Berry, E.;Chen, Y-C.;Fasy, BT.
• 通讯作者: Fasy, BT.

Moduli spaces of morse functions for persistence

持久性莫尔斯函数的模空间

• DOI: 10.1007/s41468-020-00055-x
• 发表时间: 2020
• 期刊: Journal of Applied and Computational Topology
• 作者: Catanzaro, Michael J.;Curry, Justin M.;Fasy, Brittany Terese;Lazovskis, Jānis;Malen, Greg;Riess, Hans;Wang, Bei;Zabka, Matthew
• 通讯作者: Zabka, Matthew

If You Must Choose Among Your Children, Pick the Right One

如果您必须在孩子中做出选择，请选择正确的一个

• 发表时间: 2020
• 期刊: Proceedings of the 32nd Canadian Conference on Computational Geometry (CCCG 2020
• 作者: Fasy, Brittany Terese;McCoy, Bradley;Millman, David L.
• 通讯作者: Millman, David L.